DeepONet-accelerated Bayesian inversion for moving boundary problems

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary problems, enabling their integration into digital twin platforms. To this end, a Deep Operator Network (DeepONet) architecture is employed to construct an efficient surrogate model for a moving boundary problem in single-phase Darcy flow through porous media. The surrogate enables rapid and accurate approximation of complex flow dynamics and is coupled with an Ensemble Kalman Inversion (EKI) algorithm to solve Bayesian inverse problems.The proposed inversion framework is demonstrated by estimating the permeability and porosity of fibre reinforcements for composite materials manufactured via the Resin Transfer Moulding (RTM) process. Using both synthetic and experimental in-process data, the DeepONet surrogate accelerates inversion by several orders of magnitude compared with the full-model EKI. This computational efficiency permits real-time, accurate, high-resolution estimation of local variations in permeability, porosity, and other parameters, thereby supporting effective monitoring and control of RTM processes as well as other applications involving moving boundary problems. Unlike prior approaches for RTM inversion that learn mesh-dependent mappings, the proposed DeepONet surrogate generalises across spatial and temporal domains, allowing evaluation at arbitrary sensor configurations without retraining, and represents a significant step towards practical industrial deployment of digital twins.